Deterministic Behavioural Models for Concurrency

This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled event structures, generalized trace languages in which the independence relation is context-dependent, and deterministic languages of pomsets

Relationships between Models for Concurrency

Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalized through the medium of category theory

The Limit of Splitn-Language Equivalence

AbstractSplitting is a simple form of action refinement that may be used to express the duration of actions. In particular,splitnsubdivides each action intonphases. Petri netsNandN′ aresplitn-language equivalent ifsplitn(N) andsplitn(N′) are language equivalent. It is known that these equivalences get finer and finer with increasingn. This paper characterizes the limit of this sequence by a newly defined partial order semantics. This semantics is obtained from the interval-semiword semantics, which is fully abstract for action refinement and language equivalence, by closing it under a special swap operation. The new swap equivalence lies strictly between interval-semiword and step-sequence equivalence

Finite petri nets as models for recursive causal behaviour

Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud \ud B=(a.nilb.B)+c.nil. \ud \ud We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence

Partial orders and fully abstract models for concurrency

In this thesis sets of labelled partial orders are employed as fundamental mathematical entities for modelling nondeterministic and concurrent processes thereby obtaining so-called noninterleaving semantics. Based on different closures of sets of labelled partial orders, simple algebraic languages are given denotational models fully abstract w.r.t. corresponding behaviourally motivated equivalences. Some of the equivalences are accompanied by adequate logics and sound axiomatisations of which one is complete